Radiation by solitons due to higher-order dispersion

V.I. Karpman

    Research output: Contribution to journalJournal articleResearch

    Abstract

    We consider the Korteweg-de Vries (KdV) and nonlinear Schrodinger (NS) equations with higher-order derivative terms describing dispersive corrections. Conditions of existence of stationary and radiating solitons of the fifth-order KdV equation are obtained. An asymptotic time-dependent solution to the latter equation, describing the soliton radiation, is found. The radiation train may be in front as well as behind the soliton, depending on the sign of dispersion. The change rate of the soliton due to the radiation is calculated. A modification of the WKB method, that permits one to describe in a simple and general way the radiation of KdV and NS, as well as other types. of solitons, is developed. From the WKB approach it follows that the soliton radiation is a result of a tunneling transformation of the non-linearly self-trapped wave into the free-propagating radiation.
    Original languageEnglish
    JournalPhysical Review E
    Volume47
    Issue number3
    Pages (from-to)2073-2082
    ISSN1063-651X
    DOIs
    Publication statusPublished - 1993

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